Complete integrability from Poisson Nijenhuis structures on compact hermitian symmetric spaces
For more information about this meeting, contact Ping Xu.
Speaker: Francesco Bonechi, Istituto Nazionale Fisica Nucleare - Firenze
Abstract: The so called Bruhat-Poisson structure is compatible with the Kostant-Kirillov-Souriau bracket when considered on compact hermitian symmetric spaces. This property allows the definition of a Poisson Nijenhuis structure. We study the spectrum of the Nijenhuis tensor, which proves to be non degenerate and defines a completely integrable model. On the Grassmannians this is the well known Gelfand-Cetlin model. By construction these models have a bihamiltonian description, i.e. the hamiltonians are in involution with respect to both Poisson structures. In this talk I will review the basic facts needed for this analysis, namely the construction of integrable models from collective hamiltonians (Thimm method) and Poisson vector bundles. The point of view mainly focuses on the geometry of the Bruhat-Poisson structures, in particular on its symplectic groupoid.
Room Reservation Information
Room Number: 216 McAllister
Time: 2:30pm - 3:20pm